Books by Manfred (University of South Carolina) Stoll

This comprehensive monograph is ideal for established researchers in the field and also graduate students who wish to learn more about the subject. The text is made accessible to a broad audience as it does not require any knowledge of Lie groups and only a limited knowledge of differential geometry. The author's primary emphasis is on potential theory on the hyperbolic ball, but many other relevant results for the hyperbolic upper half-space are included both in the text and in the end-of-chapter exercises. These exercises expand on the topics covered in the chapter and involve routine computations and inequalities not included in the text. The book also includes some open problems, which may be a source for potential research projects.

This monograph provides an introduction and a survey of recent results in potential theory with respect to the Laplace-Beltrami operator D in several complex variables, with special emphasis on the unit ball in Cn. The notes are self-contained, and should be accessible to anyone with some basic knowledge of several complex variables.